1. Field of the Invention
This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to the field of wavefield extrapolation in dual-sensor marine seismic streamer signals.
2. Description of the Related Art
In the oil and gas industry, geophysical prospecting is commonly used to aid in the search for and evaluation of subterranean formations. Geophysical prospecting techniques yield knowledge of the subsurface structure of the earth, which is useful for finding and extracting valuable mineral resources, particularly hydrocarbon deposits such as oil and natural gas. A well-known technique of geophysical prospecting is a seismic survey. In a land-based seismic survey, a seismic signal is generated on or near the earth's surface and then travels downward into the subsurface of the earth. In a marine seismic survey, the seismic signal may also travel downward through a body of water overlying the subsurface of the earth. Seismic energy sources are used to generate the seismic signal which, after propagating into the earth, is at least partially reflected by subsurface seismic reflectors. Such seismic reflectors typically are interfaces between subterranean formations having different elastic properties, specifically sound wave velocity and rock density, which lead to differences in acoustic impedance at the interfaces. The reflected seismic energy is detected by seismic sensors (also called seismic receivers) at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes and recorded.
The resulting seismic data obtained in performing a seismic survey is processed to yield information relating to the geologic structure and properties of the subterranean formations in the area being surveyed. The processed seismic data is processed for display and analysis of potential hydrocarbon content of these subterranean formations. The goal of seismic data processing is to extract from the seismic data as much information as possible regarding the subterranean formations in order to adequately image the geologic subsurface. In order to identify locations in the Earth's subsurface where there is a probability for finding petroleum accumulations, large sums of money are expended in gathering, processing, and interpreting seismic data. The process of constructing the reflector surfaces defining the subterranean earth layers of interest from the recorded seismic data provides an image of the earth in depth or time.
The image of the structure of the Earth's subsurface is produced in order to enable an interpreter to select locations with the greatest probability of having petroleum accumulations. To verify the presence of petroleum, a well must be drilled. Drilling wells to determine whether petroleum deposits are present or not, is an extremely expensive and time-consuming undertaking. For that reason, there is a continuing need to improve the processing and display of the seismic data, so as to produce an image of the structure of the Earth's subsurface that will improve the ability of an interpreter, whether the interpretation is made by a computer or a human, to assess the probability that an accumulation of petroleum exists at a particular location in the Earth's subsurface.
The appropriate seismic sources for generating the seismic signal in land seismic surveys may include explosives or vibrators. Marine seismic surveys typically employ a submerged seismic source towed by a ship and periodically activated to generate an acoustic wavefield. The seismic source generating the wavefield may be of several types, including a small explosive charge, an electric spark or arc, a marine vibrator, and, typically, a gun. The seismic source gun may be a water gun, a vapor gun, and, most typically, an air gun. Typically, a marine seismic source consists not of a single source element, but of a spatially-distributed array of source elements. This arrangement is particularly true for air guns, currently the most common form of marine seismic source. In an air gun array, each air gun typically stores and quickly releases a different volume of highly compressed air, forming a short-duration impulse.
The appropriate types of seismic sensors typically include particle velocity sensors, particularly in land surveys, and water pressure sensors, particularly in marine surveys. Sometimes particle displacement sensors, particle acceleration sensors, or pressure gradient sensors are used in place of or in addition to particle velocity sensors. Particle velocity sensors and water pressure sensors are commonly known in the art as geophones and hydrophones, respectively. Seismic sensors may be deployed by themselves, but are more commonly deployed in sensor arrays. Additionally, pressure sensors and particle velocity sensors may be deployed together in a marine survey, collocated in pairs or pairs of spatial arrays.
In a typical marine seismic survey, a seismic survey vessel travels on the water surface, typically at about 5 knots, and contains seismic acquisition equipment, such as navigation control, seismic source control, seismic sensor control, and recording equipment. The seismic source control equipment causes a seismic source towed in the body of water by the seismic vessel to actuate at selected locations. Seismic streamers, also called seismic cables, are elongate cable-like structures towed in the body of water by the seismic survey vessel that tows the seismic source or by another seismic survey ship. Typically, a plurality of seismic streamers is towed behind a seismic vessel.
When the air-gun array is fired, an impulse sound wave travels down through the water and into the earth. At each interface where the type of rock changes, a portion of that sound wave is reflected back toward the surface and back into the water layer. After the reflected wave reaches the streamer cable, the wave continues to propagate to the water/air interface at the water surface, from which the wave is reflected downwardly, and is again detected by the hydrophones in the streamer cable. The water surface is a good reflector and the reflection coefficient at the water surface is nearly unity in magnitude and is negative in sign for pressure waves. The pressure waves reflected at the surface will thus be phase-shifted 180 degrees relative to the upwardly propagating waves. The downwardly propagating wave recorded by the receivers is commonly referred to as the surface reflection or the “ghost” signal. Because of the surface reflection, the water surface acts like a filter, which creates spectral notches in the recorded signal, making it difficult to record data outside a selected bandwidth. Because of the influence of the surface reflection, some frequencies in the recorded signal are amplified and some frequencies are attenuated.
Maximum attenuation of the pressure wave occurs at frequencies for which the propagation distance between the detecting hydrophone and the water surface is equal to one-half wavelength. Maximum amplification occurs at frequencies for which the propagation distance between the detecting hydrophone and the water surface is one-quarter wavelength. The wavelength of the acoustic wave is equal to the velocity divided by the frequency, and the velocity of an acoustic wave in water is about 1500 meters/second. Accordingly, the location in the frequency spectrum of the resulting spectral notch is readily determinable. For example, for a seismic streamer at a depth of 7 meters, and waves with vertical incidence, maximum attenuation occurs at a frequency of about 107 Hz and maximum amplification occurs at a frequency of about 54 Hz.
A particle motion sensor, such as a geophone, has directional sensitivity, whereas a pressure sensor, such as a hydrophone, does not. Accordingly, the upgoing wavefield signals detected by a geophone and hydrophone located close together will be in phase, while the downgoing wavefield signals will be recorded 180 degrees out of phase. Various techniques have been proposed for using this phase difference to reduce the spectral notches caused by the surface reflection and, if the recordings are made on the seafloor, to attenuate water borne multiples. It should be noted that an alternative to having the geophone and hydrophone co-located, is to have sufficient spatial density of sensors so that the respective wavefields recorded by the hydrophone and geophone can be interpolated or extrapolated to produce the two wavefields at the same location.
It is well known in the art that pressure and particle motion signals can be combined to derive both the up-going and the down-going wavefield. For sea floor recordings, the up-going and down-going wavefields may subsequently be combined to remove the effect of the surface reflection and to attenuate water borne multiples in the seismic signal.
Conventional 3D marine seismic acquisition by towed streamer usually results in asymmetrical spatial sampling and fold between inline and cross-line directions. The sampling density is denser in the inline direction (parallel to the towed streamers) than in the cross-line direction (perpendicular to the towed streamers). The asymmetry is due to a wider spacing between receivers in separate streamers than between receivers in the same streamer. This asymmetry can lead to spatial aliasing of the sampling data in the cross-line direction. The aliasing interferes with conventional efforts to combine the pressure and particle motion signals to derive the up-going and down-going wavefields.
Conventionally, changing seismic data recorded from a dual-sensor streamer, towed at a receiver depth of zr meters, to another depth, z, would entail the following steps. The pressure (hydrophone) and vertical particle velocity (geophone) traces h and g, respectively, would be corrected for impulse response differences between the two types of detectors. The corrected pressure and vertical particle velocity traces contained in a common-shot gather are then transformed into the frequency-wavenumber (“FK”) domain, yielding H and G, respectively. The transformations can be done by any well-known FK transform, such as, for example, Fourier transforms. The vertical particle velocity trace amplitudes would be corrected for non-vertical arrivals of seismic waves as taught by Amundsen (in his 1993 article in Geophysics, Vol. 58, No. 9, p. 1335-1348) and, if necessary, tow noise, as taught by Vaage et al. (in their 2004 patent, U.S. Pat. No. 7,359,283 B2), yielding Gc. The upward traveling pressure wave field, U, and the downward traveling pressure wave field, D, would be computed in the FK domain, using the equations:
                              U          =                                    H              -                              G                c                                      2                          ⁢                                  ⁢        and                            (        1        )                                D        =                                            H              +                              G                c                                      2                    .                                    (        2        )            
Then, the up-going and down-going wavefields U and D from Equations (1) and (2), respectively, are extrapolated from receiver depth zr to another depth z to new up-going and down-going wavefields Unew and Dnew, respectively, using the equations;Unew=U exp[+ikz(zr−z)]  (3)andDnew=D exp[−ikz(zr−z)].   (4)Here, i=√{square root over (−1)} is the imaginary unit and kz is a vertical wavenumber given by:
                                          k            z                    =                                                                      (                                      ω                    c                                    )                                2                            -                              k                x                2                            -                              k                y                2                                                    ,                            (        5        )            where kx is a horizontal wavenumber, in the streamer (inline) direction, computed by the FK transform; ky is a horizontal wavenumber, in the cross-streamer (cross-line) direction, also computed by the FK transform; co is radian frequency; and c is acoustic wave propagation velocity in water. Finally, these new corrected wavefields Unew and Dnew from Equations (3) and (4), respectively, are inverse-transformed back to the space-time domain. Note that signals in the time domain are denoted by lower case letters, while the same signals in the frequency domain are denoted by the corresponding capital letters.
This conventional wavefield correction is accurate, but depends upon all the receiver stations being towed at the same depth and the recording geometry being such that the traces comprising a common-shot record are not spatially aliased in the x or y dimensions. If either of these assumptions is violated, the results of the above described operation are compromised.
Thus, a need exists for a method for extrapolating up-going and down-going wavefields in dual-sensor seismic streamer data from a single receiver station, which accounts for vertical (depth) variation and horizontal spatial aliasing of the receiver positions.